Topology optimization offers lightweight and high-performance solutions for structural design. With the rapid advancement of neural networks, topology optimization methods leveraging neural architectures have gained increasing attention. Among these methods, positional encoding is crucial for enabling neural networks to capture high-frequency geometry features, making its integration into neural network-based optimization methods a promising direction for exploration. This paper focuses on positional encoding by introducing a spline-based positional encoding into the neural topology optimization framework, in which spatial coordinates are transformed using spline basis functions before being input into the neural network. The performance of different classic spline basis functions is comprehensively evaluated, including the Bézier spline, B-spline, and NURBS spline. Experimental results demonstrate that positional encoding based on quadratic B-spline basis functions yields the highest structural stiffness. To further validate the effectiveness of the proposed method, a comparative analysis is performed against Fourier and super-Gaussian positional encoding schemes. The results show that spline-based encoding outperforms both alternatives in terms of structural compliance in most cases. Moreover, the resulting topologies exhibit smooth boundaries, free from oscillations and superfluous geometric details.
Drawing on industry convergence theory, this study develops an evaluation index system to quantify cultural-tourism integration. It applies the entropy weight method and a multiple-linear comprehensive index approach to measure both the levels and the spatiotemporal dynamics of culture-tourism integration in 31 selected Chinese provinces (municipalities and autonomous regions) from 2010 to 2022. A staggered Difference-in-Differences model is then used to estimate the driving effects of integration policies and to uncover the pathways. The results show a steady upward trend in integration, marked regional disparities consistent with a Matthew effect, and a significant overall policy effect on integration levels, with notable heterogeneity across regions. Pathways analysis indicates that policies primarily enhance resource and market integration and that the pathways of policies also influence differ by region. This study advances understanding of how policy drives cultural-tourism integration and provides guidance for promoting high-quality, balanced regional development of culture-tourism.
Existing studies on the bidding dilemma in electricity markets mostly adopt mandatory participation and rarely integrate reputation effects. To fill this gap, this paper proposes reputation-driven Q-learning as a solution to the bidding dilemma between heterogeneous generation groups, developing a coupled evolutionary model of reputation, strategy, and voluntary participation. The authors examine 256 social norms under low, medium, and high demand scenarios. Results show that the synergy of reputation and voluntary participation significantly outperforms mandatory participation: It supports more social norms and promotes cooperative high-bidding by rewarding good-reputation generation companies (GENCOs) and punishing bad-reputation ones, whereas mandatory participation only works under limited norms and often relies on unfair reward-punishment rules. The authors further reveal the phase-transition patterns of cooperative high-bidding under different social norms, which provides clear guidance for designing low-cost market mechanisms. The proposed reputation-driven Q-learning mechanism can achieve spontaneous market cooperation without heavy administrative intervention, thus reducing regulatory costs and improving market efficiency.
In practice, data often contain outliers, which can significantly distort the results of traditional statistical methods. Meanwhile, in some practical problems, the proposed objective is to precisely identify outliers. Therefore, it is necessary to perform outlier detection before or in data analysis. The use of auxiliary information generally improves the performance of statistical methods. Building on this idea, a ratio estimator for the Median Absolute Deviation (MAD) is constructed, and its consistency is proven. Based on this estimator, the authors develop novel outlier detection methods that incorporate auxiliary variables into the MAD framework. Simulation results demonstrate that the proposed method outperforms some commonly used outlier detection techniques. An application to the “Body and Brain Weight” dataset also shows the merit of the proposed method.
The operation of a microgrid (MG) system with multiple nodes not only needs to solve the optimization problem of economic dispatch but also has to consider the optimization goals of the safe and environmentally friendly operation. Therefore, the purpose of each node with renewable resources is to collaborate to achieve the optimization of multiple objectives. In this paper, the authors shall design a deep reinforcement learning (DRL) algorithm to perform the multi-objective optimization which can handle continuous action space and determine the specific output power of each device. Unlike the existing algorithms that learn policies with holistic reward signals, the proposed algorithm decomposes the reward into multiple parts and trains multiple critic networks for sub-objectives to get the Pareto optimal solutions. The proposal of single-actor multi-critic architecture not only can avoid task-specific local optimal policies but also does not need to set weight values. The effectiveness of the algorithm is verified by case studies on a modified IEEE-30 bus system and a modified IEEE-118 bus system. After training, the DRL agent can adapt to the high uncertainty of the photovoltaics and exploit the capacity of battery energy storage stations safely, which is more practical in a real system.
This paper presents an optimization method based on optimal control for finding multiple local minimum points of non-convex objective functions. The authors reformulate the original optimization problem (OP) as an optimal control problem and solve it using numerical algorithms to obtain the state trajectory of the system, which approaches the local minimum point of the original objective function in a fast and stable way. The proposed method is capable of identifying multiple local minimum points within a single optimization process and escaping saddle points by strategically designing the initial control sequence in numerical algorithms. Furthermore, the convexity of the optimal control problem can be ensured by choosing the control weight matrix, providing a novel perspective for solving non-convex OPs. Finally, the authors demonstrate that the proposed method exhibits high accuracy, low oscillation, and more stability in non-convex settings, highlighting its practicality and potential in tackling complex optimization tasks.
Elliptic curves over finite fields have been extensively used to build public key cryptography (a.k.a. Elliptic Curve Cryptography (ECC)). The choice of elliptic curves significantly affects the security and performance of the relevant cryptosystem. At present, standardized curves in ECC are all defined over finite fields of characteristic 2 or large prime characteristic, while those of characteristic 3 have drawn little attention mainly due to their lower efficiency in implementation. In this work, the authors primarily study ordinary elliptic curves defined over the quadratic extension field of characteristic 3 equipped with the Frobenius endomorphism. All relevant operations of finite field and elliptic curves, implemented by the AVX2 instructions and 256-bit wide SIMD operands, are developed and optimized to ensure both efficient and constant-time execution. At the 128-bit security level, the proposed implementation is approximately 1.8 times faster than the previous work for scalar multiplication on ordinary curves of characteristic 3. To the best of our knowledge, this is the first scalar multiplication implementation on elliptic curves of characteristic 3 which outperforms those on standard curves such as NIST P-256 and SM2.
NMDS codes and MDS codes have critical theoretical and practical value. In this paper, the authors develop a general construction of 3-dimensional NMDS codes of lengths from 2m to 2m+2 by selecting suitable generator matrices and determine their weight enumerators, where m ≥ 2 is an integer. In particular, the authors construct two types of 3-dimensional MDS codes and analyze the properties of the subfield codes of one of them. Then the authors derive some optimal locally recoverable codes via the NMDS codes. It is worth noting that all the NMDS and MDS codes are near Griesmer and Griesmer codes, respectively. Furthermore, the duals of the NMDS codes achieve length and dimension optimality, and of the MDS codes achieve distance optimality under the sphere packing bound. Finally, the authors use some of the codes constructed to build s-sum sets (where s > 1 is odd), strongly regular graphs and 3-designs.
This work considers a stochastic epidemic model with general incidence rates incorporating an Ornstein–Uhlenbeck driven transmission rate. The authors establish the uniqueness of the global solution. The authors then prove the model’s geometric ergodicity, and provide a mild condition under which the model converges to a unique stationary distribution around the equilibrium. Because the transition density of this system is analytically intractable, the authors employ a stationary Gaussian pseudo maximum likelihood estimation approach and profile likelihood methods for parameter estimation and confidence intervals. A subsampling method for sampling near-independent observations from time trajectories is proposed. The theoretical reliability of this subsampling method is established through rigorous proof. Numerical experiments are provided to illustrate the theoretical results.
This paper investigates the exponential synchronization problem for a class of nonlinear directed networks with time delays and general unknown transition rates. The considered model incorporates time-delays, directed topological structures, and uncertain transition rates, where the transition rates can be either completely unknown or only partially estimated. A distributed controller is designed within a novel pull-based event-triggered sampling framework, ensuring that the closed-loop system achieves exponential synchronization while significantly reducing the update frequencies of sensors and controllers with performance guarantees. By estimating a positive lower bound for event intervals, the proposed event-triggered schemes effectively exclude Zeno behavior. Event-triggered parameters are systematically designed based on the feasibility conditions of associated matrix inequalities. Numerical simulations are provided to validate the theoretical findings, demonstrating the effectiveness and practical applicability of the proposed approach.
High-dimensional linear mixed models are widely used for longitudinal data analysis, yet their reliance on normality assumptions often limits applicability in psychometric and biomedical settings. To address this, the authors propose a high-dimensional skew-normal linear mixed model and develop a novel variational Baysian method that integrates spike-and-slab Lasso priors for simultaneous parameter estimation and variable selection. To handle dependencies in the joint posterior, the authors propose a variational auto-encoders to extract latent features, and employ a coordinate ascent algorithm to optimize the evidence lower bound (ELBO), circumventing intractable integrals. Model comparison is conducted using the Bayes factor, approximated via the ELBO. The effectiveness of the proposed methodologies is demonstrated through simulation studies and a real-data application.
To estimate physical parameters in a grey-box model with linear regressions, a two-step approach with much reduced computational complexity is developed. First, the parameters of the linear regression model are estimated via the simple linear least square method, before they are fed into a nonlinear optimization problem of a much reduced dimension. It is discovered that the right formulation of the optimization criterion depends on the input-output data, and can be expressed in terms of the singular value decomposition of the data matrix. It is also found that the estimated physical parameters can be fed back to improve the parameters of the linear regression model. This improvement is a consequence of exploiting the structural information of the system contained in the grey-box model, and thus overfitting to the limited training data can be avoided. Numerical examples are presented to demonstrate the effectiveness of the approach.
Monotonic optimization is a special class of global optimization with applications cross fields. It addresses problems in which the objective and constraint functions are increasing w.r.t. each of the variables. In this work, the authors extend to the case where the objective and constraint functions are monotonic. The authors present a general framework to address such problems, and especially propose a complete algorithm that is guaranteed to terminate in finitely many steps for problems in a special form. Different from traditional optimization algorithms based on gradient descent, the proposed algorithm does not require closed-form expressions of the functions. As an important application, the functions involved in the parameter optimization problem of LWE-based encryption scheme exhibit monotonicity w.r.t. each of the variables (but may not be increasing), and certain functions involved have no closed-form expression. Inspired by the idea of mathematics mechanization, the authors formalize practical problems into mathematical models and provide a framework for developing automatic and systematic approaches to tackle the parameter optimization problems in lattice-based cryptography. As an illustrative example, the authors consider the parameter optimization of BGV scheme in the context of minimizing communication overhead, without considering homomorphic operations, and provide optimal parameters for it under specified security levels and correctness probabilities.
The map search data, which reflect the willingness to travel, have the potential in forecasting tourist arrivals. This study introduces the map search data as a new indicator in tourist arrivals forecasting. The authors use Mount Tai and Macao, China’s daily tourist arrival data as experimental data and the map search volume index. By employing four widely-used methods, the authors use the map search data and search engine data as indicators in tourist arrivals forecasting. The experimental results show that the map search data can effectively improve forecasting performance, which is better than using search engine data. These findings are still valid during the COVID-19 pandemic by examining them in Macao, China’s data.
Space-filling designs are widely used in computer experiments to build effective metamodels with limited prior information, as they enable thorough exploration of the design space by uniformly distributing points. However, many existing designs perform poorly in low-dimensional projections, particularly when only a few factors are active. Uniform projection designs address this limitation by optimizing point distribution across low-dimensional subspaces, ensuring uniformity in all dimensions while maintaining desirable distance and column-orthogonality properties. Existing methods for constructing such designs often rely on complex algorithms or can only generate designs with large factor-to-run ratios. In this work, the authors propose a simple approach for constructing uniform projection Latin hypercube designs by employing orthogonal arrays. The proposed method is particularly effective when the number of factors is much smaller than the number of runs. Both theoretical and numerical results demonstrate that the designs produced by the proposed method perform well with respect to the uniform projection, low-dimensional stratification, maximin distance, and column-orthogonality criteria.
In this paper, the authors stumble upon that the normal ordering expansion for (xddx)^n is equivalent to the expansion of (bDG)n, where G is the context-free grammar defined by G = a → a, b → 1. Motivated by this fact, the authors introduce the definition of grammatical basis. The authors then study several grammatical bases generated by G = a → 1, b → 1. Using grammatical bases, the authors give a classification of grammars. In particular, the authors provide new grammatical descriptions for Ward numbers, Hermite polynomials, Bessel polynomials, Chebyshev polynomials and logarithmic polynomials arising from an integral. The authors end this paper by giving some applications of grammatical bases. One can see that if two or more polynomials share a grammatical basis, then they share the same coefficients, and it might be helpful for the detection of intrinsic relationship among superficially different structures.
With the advancement of modern information technology, the collection and analysis of multi-source time series data play an important role in decision-making and process management. However, due to the complexity of capturing the dynamic features for spatio-temporal information, multi-source time series forecasting remains a challenging problem. Previous spatio-temporal models usually overlook the integration of physical and spatial dependencies between multivariable data features, as well as the effects of dynamic diffusion. To address these challenges, the authors propose a Spatio-Temporal Information Dual-layer Diffusion Network (STIDDN) for multi-source time series collaborative forecasting. STIDDN employs residual LSTM networks for temporal dependency modeling of internal features at each station, while the Dual-layer Diffusion Graph Convolutional Network (Dual-DGCN) focuses on capturing both physical and spatial dual-layer dependencies between stations, along with the dynamic diffusion process. By integrating spatio-temporal information through a skip-connection and multi-head attention mechanism, STIDDN achieves effective collaborative forecasting across multiple stations. Extensive experimental results demonstrate that the proposed model consistently outperforms advanced baseline models on two different spatio-temporal prediction task datasets.
This paper is dedicated to studying the event-based consensus tracking control problem of leader-following multi-agent systems under hybrid attacks. First, different from conventional event-triggered mechanisms, a dynamic memory event-triggered mechanism is designed to decrease the frequency of communication between agents, which relies on historical error data and instantaneous error data and considers the cumulative impact of historical data on the system. Then, an improved asymmetric Lyapunov-Krasovskii function is presented. Based on the integral inequality and Lyapunov theorem, some stability conditions of multi-agent systems under hybrid attacks are obtained by solving linear matrix inequality. Finally, two simulation examples are given to verify the feasibility and superiority of the proposed method.
This work investigates prescribed-time flocking control with collision avoidance for Cucker-Smale systems. The authors propose a novel control framework that guarantees prescribed-time flocking, with convergence time that are both independent of initial conditions and control parameters. Within the framework of Lyapunov stability theory, the authors derive sufficient conditions guaranteeing both flocking convergence and collision avoidance in Cucker-Smale systems. In addition, an upper bound for the energy required to achieve flocking is theoretically derived. The results indicate that parameters α and β significantly affect the system’s flocking dynamics. Specifically, parameter α exhibits a nonmonotonic relationship with convergence speed and energy cost, revealing a fundamental performance trade-off. In contrast, reducing parameter β simultaneously improves convergence speed and decreases energy cost. Furthermore, the prescribed time Tp and system size N are critical factors that substantially affect energy consumption. The results provide theoretical foundations for designing efficient flocking controllers and balancing the trade-off between convergence speed and energy cost.
